Dear PF Forum,(adsbygoogle = window.adsbygoogle || []).push({});

I'd like to study integral.

But I just realize that I'm lack of basic integral.

Can I ask here?

Let y=x^{2}

Here is the graph.

So,

1. dx is the distance between the red vertical lines? But it's very, very, very small distance.

2. f(x) * dx is the yellow area?

3. ##\int_0^2 x^2\,dx## is the green (plus yellow) area?

4. And one more thing. The blue line function can be derived from the derivative of f(x)?

For example the derivative of x^{2}is 2x. So a line that crosses (x,f(x)) where x=1 is 2.

The blue line function is y = 2x.

If it crosses (x,f(x)) where x = 2, then the blue line function is y = 4x?

Thank you very much

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# B Basic integral

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